Finite Representation of Quantile Sets for Multivariate Data via Vector Linear Programming
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913328324935680 |
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| author | Löhne, Andreas Weißing, Benjamin |
| author_facet | Löhne, Andreas Weißing, Benjamin |
| contents | Empirical quantiles for finitely distributed univariate random variables can be obtained by solving a certain linear program. It is shown in this short note that multivariate empirical quantiles can be obtained in a very similar way by solving a vector linear program. This connection provides a new approach for computing Tukey depth regions and more general cone quantile sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15600 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite Representation of Quantile Sets for Multivariate Data via Vector Linear Programming Löhne, Andreas Weißing, Benjamin Statistics Theory Optimization and Control 62H10, 90C29 Empirical quantiles for finitely distributed univariate random variables can be obtained by solving a certain linear program. It is shown in this short note that multivariate empirical quantiles can be obtained in a very similar way by solving a vector linear program. This connection provides a new approach for computing Tukey depth regions and more general cone quantile sets. |
| title | Finite Representation of Quantile Sets for Multivariate Data via Vector Linear Programming |
| topic | Statistics Theory Optimization and Control 62H10, 90C29 |
| url | https://arxiv.org/abs/2303.15600 |